TSTP Solution File: FLD035-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD035-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 02:28:25 EDT 2022
% Result : Unsatisfiable 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 24 ( 12 unt; 1 nHn; 24 RR)
% Number of literals : 44 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
defined(b),
file('FLD035-3.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD035-3.p',unknown),
[] ).
cnf(5,axiom,
product(a,c,u__dfg),
file('FLD035-3.p',unknown),
[] ).
cnf(6,axiom,
product(b,c,u__dfg),
file('FLD035-3.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,c,additive_identity),
file('FLD035-3.p',unknown),
[] ).
cnf(8,axiom,
~ product(multiplicative_identity,a,b),
file('FLD035-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD035-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD035-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD035-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD035-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD035-3.p',unknown),
[] ).
cnf(37,plain,
( ~ product(b,u,v)
| ~ product(c,w,u)
| product(u__dfg,w,v) ),
inference(res,[status(thm),theory(equality)],[6,15]),
[iquote('0:Res:6.0,15.0')] ).
cnf(49,plain,
( ~ product(u__dfg,u,v)
| ~ product(c,u,w)
| product(a,w,v) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.0,14.0')] ).
cnf(61,plain,
~ product(a,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[18,8]),
[iquote('0:Res:18.1,8.0')] ).
cnf(65,plain,
( ~ defined(c)
| product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[17,7]),
[iquote('0:Res:17.2,7.0')] ).
cnf(73,plain,
product(multiplicative_inverse(c),c,multiplicative_identity),
inference(mrr,[status(thm)],[65,3]),
[iquote('0:MRR:65.0,3.0')] ).
cnf(93,plain,
product(c,multiplicative_inverse(c),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[73,18]),
[iquote('0:Res:73.0,18.0')] ).
cnf(94,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[16,18]),
[iquote('0:Res:16.1,18.0')] ).
cnf(360,plain,
( ~ defined(b)
| ~ product(c,u,multiplicative_identity)
| product(u__dfg,u,b) ),
inference(res,[status(thm),theory(equality)],[94,37]),
[iquote('0:Res:94.1,37.0')] ).
cnf(365,plain,
( ~ product(c,u,multiplicative_identity)
| product(u__dfg,u,b) ),
inference(ssi,[status(thm)],[360,2]),
[iquote('0:SSi:360.0,2.0')] ).
cnf(404,plain,
product(u__dfg,multiplicative_inverse(c),b),
inference(res,[status(thm),theory(equality)],[93,365]),
[iquote('0:Res:93.0,365.0')] ).
cnf(411,plain,
( ~ product(c,multiplicative_inverse(c),u)
| product(a,u,b) ),
inference(res,[status(thm),theory(equality)],[404,49]),
[iquote('0:Res:404.0,49.0')] ).
cnf(417,plain,
product(a,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[93,411]),
[iquote('0:Res:93.0,411.0')] ).
cnf(421,plain,
$false,
inference(mrr,[status(thm)],[417,61]),
[iquote('0:MRR:417.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD035-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 6 14:57:58 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.22/0.52
% 0.22/0.52 SPASS V 3.9
% 0.22/0.52 SPASS beiseite: Proof found.
% 0.22/0.52 % SZS status Theorem
% 0.22/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.52 SPASS derived 346 clauses, backtracked 0 clauses, performed 0 splits and kept 291 clauses.
% 0.22/0.52 SPASS allocated 76015 KBytes.
% 0.22/0.52 SPASS spent 0:00:00.15 on the problem.
% 0.22/0.52 0:00:00.04 for the input.
% 0.22/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.52 0:00:00.01 for inferences.
% 0.22/0.52 0:00:00.00 for the backtracking.
% 0.22/0.52 0:00:00.08 for the reduction.
% 0.22/0.52
% 0.22/0.52
% 0.22/0.52 Here is a proof with depth 5, length 24 :
% 0.22/0.52 % SZS output start Refutation
% See solution above
% 0.22/0.52 Formulae used in the proof : b_is_defined c_is_defined product_5 product_6 not_sum_7 not_product_8 associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication
% 0.22/0.52
%------------------------------------------------------------------------------